Yes, Quantum Field Theory (QFT) takes into account the wave nature of particles. In QFT, particles are understood as excitations of underlying quantum fields that permeate space. These fields are described by wave-like mathematical functions known as quantum field operators.
In QFT, each type of particle corresponds to a specific quantum field. For example, the electromagnetic field is associated with photons, the electron field is associated with electrons, and so on. These fields are defined throughout spacetime, and the excitations or disturbances of these fields are what we observe as particles.
The wave-like nature of particles emerges from the underlying quantum fields. Just as a wave in classical physics carries energy and momentum, the excitations of quantum fields in QFT can also be thought of as carrying energy, momentum, and other properties. However, it's important to note that these waves are not waves in physical space but rather waves in the mathematical space of the quantum fields.
Regarding the concept of position, in Quantum Field Theory, the notion of precise position becomes less well-defined compared to classical physics. This is due to the Heisenberg uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known.
In QFT, instead of thinking of particles as having well-defined positions, we typically describe them in terms of probability distributions. The quantum field operators provide information about the likelihood of finding a particle at different positions or momenta. The excitations of the field can be understood as localized disturbances or events occurring within the field, but the exact position of a particle is not determined until a measurement is made.
In summary, Quantum Field Theory incorporates the wave nature of particles through the description of particles as excitations of underlying quantum fields. The wave-like behavior arises from the mathematical properties of these fields, while the exact position of a particle is generally described in terms of probabilities rather than precise values.